Eliminating a variable and then optimizing through differentiation

The goal here is to find the value of Ө, in terms of Ф, that results in the maximum possible value of d. We start with the following equations:

x = (vcosӨ)t = dcosФ
y = (vsinӨ)t - (1/2)gt2 = -dsinФ
d = √(x2 + y2)

Originally Posted by My Textbook

By eliminating the variable t between these equations and using differentiation to maximize d in terms of

Originally Posted by My Textbook

Ө, we arrive at the following equation for the angle Ө that gives the maximum value of d:Ө = 45º - Ф/2

My question is, what exactly are the steps in eliminating t and then using differentiation to maximize d? I suspect that I'm supposed to solve one of the equations for t (e.g., t = (dcosФ)/(vcosӨ) or t = x/(vcosӨ))and then plug that t into the other equation. But is that right? And if so, what do I do next?

By the way, that awkward double-quote isn't my mistake, it's some kind of weird bug.